[3.12] gh-91053: make func watcher tests resilient to other func watchers (GH-106286) (#106365)

gh-91053: make func watcher tests resilient to other func watchers (GH-106286)
(cherry picked from commit 58906213cc5d8f2be311664766b4923ef29dae1f)

Co-authored-by: Carl Meyer <carl@oddbird.net>